Differential Equations

Differential Equations

For Any Real Numbers α and β, Let y(α,β)(x) Be the Solution of dy/dx + αy = xe^(βx), y(1) = 1. If S = {y(α,β)(x) : α, β ∈ R}, Then Which of the Following Functions Belong to S
ByShiwam October 5, 2026September 16, 2026

For real α, β let y_{α,β}(x) solve dy/dx+αy=xe^(βx), y(1)=1. S is the set of all such functions. Which given options belong to S? Multiple correct.

Read More For Any Real Numbers α and β, Let y(α,β)(x) Be the Solution of dy/dx + αy = xe^(βx), y(1) = 1. If S = {y(α,β)(x) : α, β ∈ R}, Then Which of the Following Functions Belong to S
Differential Equations

Let the Solution Curve y = y(x) of dy/dx − 3x⁵tan⁻¹(x³)y/(1+x⁶)^(3/2) = 2x·exp((x³−tan⁻¹x³)/√(1+x⁶)) Pass Through the Origin. Then y(1) Is Equal To
ByShiwam October 2, 2026September 16, 2026

The solution curve y=y(x) of dy/dx − 3x⁵tan⁻¹(x³)y/(1+x⁶)^(3/2) = 2x·exp[(x³−tan⁻¹x³)/√(1+x⁶)] passes through the origin. Find y(1).

Read More Let the Solution Curve y = y(x) of dy/dx − 3x⁵tan⁻¹(x³)y/(1+x⁶)^(3/2) = 2x·exp((x³−tan⁻¹x³)/√(1+x⁶)) Pass Through the Origin. Then y(1) Is Equal To
Differential Equations

The Solution of the Differential Equation cos x·dy = y(sin x − y)dx, for 0 < x < π/2, Is
ByShiwam September 26, 2026September 16, 2026

Solve the differential equation cos x dy = y(sin x − y)dx for x in (0,π/2), by recognising it as a Bernoulli equation and substituting t=1/y.

Read More The Solution of the Differential Equation cos x·dy = y(sin x − y)dx, for 0 < x < π/2, Is
Differential Equations

y=(x−y dx/dy)sin(x/y), x(1)=π/2 — Find cos(x(2))
ByShiwam September 12, 2026September 22, 2026

Solve the differential equation y=(x−y dx/dy)sin(x/y) with x(1)=π/2, using the substitution v=x/y to reduce it to a separable equation.

Read More y=(x−y dx/dy)sin(x/y), x(1)=π/2 — Find cos(x(2))